Quantification In logic, quantification is the binding of a variable ranging over a domain of discourse. The variable thereby becomes bound by an operator called a quantifier. Academic discussion of quantification refers more often to this meaning of the term than the preceding one. Natural language[edit] All known human languages make use of quantification (Wiese 2004). Every glass in my recent order was chipped.Some of the people standing across the river have white armbands.Most of the people I talked to didn't have a clue who the candidates were.A lot of people are smart. The words in italics are quantifiers. The study of quantification in natural languages is much more difficult than the corresponding problem for formal languages. Montague grammar gives a novel formal semantics of natural languages. Logic[edit] In language and logic, quantification is a construct that specifies the quantity of specimens in the domain of discourse that apply to (or satisfy) an open formula. Mathematics[edit] . means
Interpretation From Wikipedia, the free encyclopedia Interpretation may refer to: Culture[edit] Aesthetic interpretation, an explanation of the meaning of a work of artAllegorical interpretation, an approach that assumes a text should not be interpreted literallyDramatic Interpretation, an event in speech and forensics competitions in which participants perform excerpts from playsHeritage interpretation, communication about the nature and purpose of historical, natural, or cultural phenomenaInterpretation (music), the process of a performer deciding how to perform music that has been previously composedLanguage interpretation, the facilitation of dialogue between parties using different languagesLiterary theory, broad methods for interpreting literature, including historicism, feminism, structuralism, deconstruction Literary criticism, interpretation of particular works of literatureOral interpretation, a dramatic art Law[edit] Math and computing[edit] Media[edit] Neuroscience[edit] Philosophy[edit]
Domain of discourse The term universe of discourse generally refers to the collection of objects being discussed in a specific discourse. In model-theoretical semantics, a universe of discourse is the set of entities that a model is based on. The concept universe of discourse is generally attributed to Augustus De Morgan (1846) but the name was used for the first time in history by George Boole (1854) on page 42 of his Laws of Thought in a long and incisive passage well worth study. Boole's definition is quoted below. The concept, probably discovered independently by Boole in 1847, played a crucial role in his philosophy of logic especially in his stunning principle of wholistic reference. A database is a model of some aspect of the reality of an organisation. Boole’s 1854 Definition[edit] See also[edit] References[edit] Jump up ^ Corcoran, John.
Analytic–synthetic distinction Semantic distinction in philosophy While the distinction was first proposed by Immanuel Kant, it was revised considerably over time, and different philosophers have used the terms in very different ways. Furthermore, some philosophers (starting with Willard Van Orman Quine) have questioned whether there is even a clear distinction to be made between propositions which are analytically true and propositions which are synthetically true.[2] Debates regarding the nature and usefulness of the distinction continue to this day in contemporary philosophy of language.[2] Kant[edit] Conceptual containment[edit] The philosopher Immanuel Kant uses the terms "analytic" and "synthetic" to divide propositions into two types. analytic proposition: a proposition whose predicate concept is contained in its subject conceptsynthetic proposition: a proposition whose predicate concept is not contained in its subject concept but related Examples of analytic propositions, on Kant's definition, include: [edit]
Logical truth A logical truth is considered by some philosophers to be a statement which is true in all possible worlds. This is contrasted with facts (which may also be referred to as contingent claims or synthetic claims) which are true in this world, as it has historically unfolded, but which is not true in at least one possible world, as it might have unfolded. The proposition "If p and q, then p" and the proposition "All married people are married" are logical truths because they are true due to their inherent structure and not because of any facts of the world. Later, with the rise of formal logic a logical truth was considered to be a statement which is true under all possible interpretations. The existence of logical truths has been put forward by rationalist philosophers as an objection to empiricism because they hold that it is impossible to account for our knowledge of logical truths on empiricist grounds. Logical truths and analytic truths[edit] Truth values and tautologies[edit]
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.[4] From 1939–1947, Wittgenstein taught at the University of Cambridge.[5] During his lifetime he published just one slim book, the 75-page Tractatus Logico-Philosophicus (1921), one article, one book review and a children's dictionary.[6] His voluminous manuscripts were edited and published posthumously. Philosophical Investigations appeared as a book in 1953 and by the end of the century it was considered an important modern classic.[7] Philosopher Bertrand Russell described Wittgenstein as "the most perfect example I have ever known of genius as traditionally conceived; passionate, profound, intense, and dominating".[8] Born in Vienna into one of Europe's richest families, he inherited a large fortune from his father in 1913. Background[edit] The Wittgensteins[edit]
Ambiguity Type of uncertainty of meaning in which several interpretations are plausible The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with vague information it is difficult to form any interpretation at the desired level of specificity. Linguistic forms[edit] Ambiguity in human language is argued to reflect principles of efficient communication.[2][3] Languages that communicate efficiently will avoid sending information that is redundant with information provided in the context. This can be shown mathematically to result in a system that is ambiguous when context is neglected. Lexical ambiguity[edit] The context in which an ambiguous word is used often makes it clearer which of the meanings is intended. More problematic are words whose multiple meanings express closely related concepts. Semantic and syntactic ambiguity[edit] Philosophy[edit] Expressions[edit] . .
Tractatus Logico-Philosophicus The Tractatus Logico-Philosophicus (widely abbreviated and cited as TLP) (Latin for Logical Philosophical Treatise or Treatise on Logic and Philosophy) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal: to identify the relationship between language and reality and to define the limits of science.[1] It is recognized by philosophers as a significant philosophical work of the twentieth century. G. Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it during a military leave in the summer of 1918.[3] It was first published in German in 1921 as Logisch-Philosophische Abhandlung. The Tractatus employs an austere and succinct literary style. Wittgenstein's later works, notably the posthumously published Philosophical Investigations, criticised many of his earlier ideas in the Tractatus. Main theses[edit] Proposition 1[edit] , where
Consequent Hypothetical proposition component Examples: If , then . is the consequent of this hypothetical proposition. If is a mammal, then is an animal. Here, " is an animal" is the consequent. If computers can think, then they are alive. "They are alive" is the consequent. The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent. If monkeys are purple, then fish speak Klingon. "Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple. See also[edit] References[edit]
Logical constant From Wikipedia, the free encyclopedia In logic, a logical constant or constant symbol of a language One of the fundamental questions in the philosophy of logic is "What is a logical constant?";[1] that is, what special feature of certain constants makes them logical in nature?[2] Some symbols that are commonly treated as logical constants are: Many of these logical constants are sometimes denoted by alternate symbols (for instance, the use of the symbol "&" rather than "∧" to denote the logical and). See also[edit] References[edit] External links[edit] Stanford Encyclopedia of Philosophy entry on logical constants
Logical connective The most common logical connectives are binary connectives (also called dyadic connectives) which join two sentences which can be thought of as the function's operands. Also commonly, negation is considered to be a unary connective. A logical connective is similar to but not equivalent to a conditional operator. [1] In language[edit] Natural language[edit] A: Jack went up the hill. B: Jill went up the hill. C: Jack went up the hill and Jill went up the hill. D: Jack went up the hill so Jill went up the hill. The words and and so are grammatical conjunctions joining the sentences (A) and (B) to form the compound sentences (C) and (D). Various English words and word pairs express logical connectives, and some of them are synonymous. The word "not" (negation) and the phrases "it is false that" (negation) and "it is not the case that" (negation) also express a logical connective – even though they are applied to a single statement, and do not connect two statements. Formal languages[edit] , and .